Relation between Coordinates of Vertices

Q.

What will be the centroid of a triangle whose vertices are (2, 4), (6, 4) and (2, 0)?

1. $\frac{8}{3},\frac{5}{3}$
2. $\frac{7}{2},\frac{5}{2}$
3. $\frac{10}{3},\frac{8}{3}$
4. $\frac{4}{3},\frac{2}{3}$

Q.

$A(-3,-3),B(2,-2),C(2,3)$ and $D(-4,4)$ are the vertices of quadrilateral $ABCD$. Then the point of intersection of its diagonals is

1. $(\frac{3}{11},\frac{-3}{11})$

2. $(\frac{-3}{11},\frac{-3}{11})$

3. $(\frac{-3}{11},\frac{3}{11})$

4. $(\frac{3}{11},\frac{3}{11})$

Q. Question 160
Quadrilateral EFGH is a rectangle in which J is the point of intersection of the diagonals. Find the value of x, if JF = 8x + 4 and EG = 24x - 8.

Q. $\frac{a}{x}-\frac{b}{y}=0$
$\frac{a{b}^2}{x}+\frac{a^{2}b}{y}=a^2+b^2$

1. $x=ab$ and $y=b$
2. $x=b-a$ and $y=ab$
3. $x=a$ and $y=b$
4. $x=b$ and $y=a$

Q. Question 6
Ayush starts walking from his house to office. Instead of going to the office directly, he goes to a bank first, from there to his daughter’s school and then reaches the office. What is the extra distance travelled by Ayush in reaching his office? (Assume that all distance covered are straight lines). If the house is situated at (2, 4), bank at(5, 8), school at (13, 14) and office at (13, 26) and coordinates are in km.

Q.

Kevin hired a cab and followed the path as shown in the figure. if all the distances in the figure are in kilometres. The difference between the total distance and displacement covered by him is ___ km.

Q. The area of triangle is $\frac{3}{2}$ sq units.Two of this vertices are the points $A(2,-3)$ and $B(3,-2)$, the centroid of the triangle lies on the line $3x-y-8=0$. Find the third vertex .

1. $(1,-1)$
2. $(-2,-10)$
3. or $(-2,10)$
4. None of these

Q.

Find the coordinates of the centroid of a triangle whose vertices are (0, 6), (8, 12) and (8, 0). [2 MARKS]

Q. In the following figure, $ABCD$ is a parallelogram. Find the values of $x$.

1. $5$
2. $3$
3. $9$
4. $7$

Q. A right triangle is formed by connecting the 3 coordinates A, B and C. Find the area of the $\Delta ABC$, if AB and BC are parallel to the coordinate axes as shown in the figure.

1. 6 sq. units
2. 10 sq. units
3. 12 sq. units
4. 20 sq. units

Q. The equations to a pair of opposite sides of a parallelogram are $x^2-5x+6=0and{y}^2-6y+5=0$ the equation of a diagonal can be

1. $y=4x-7$
2. $x+4y=13$
3. $4x+y=13$
4. $y=4x+7$

Q. If a vertex of a triangle is $(1,1)$ and the mid points of two sides through this vertex are $(-1,2)$ and $(3,2)$, then the centroid of the triangle is

1. $\left(\frac{-1}{3},\frac{7}{3}\right)$
2. $\left(\frac{1}{3},\frac{7}{3}\right)$
3. $(-1,\frac{7}{3})$
4. $(1,\frac{7}{3})$

Q.

A(-2, -1), B(0, -3), C(1, 0) and D(-1, 1) are the vertices of quadrilateral ABCD. Then the point of intersection of its diagonals is

1. $(\frac{8}{13},\frac{-7}{13})$

2. $(\frac{-8}{13},\frac{-7}{13})$

3. $(\frac{-3}{11},\frac{7}{13})$

4. $(\frac{3}{13},\frac{7}{11})$

Q. The $x$ and $y$ intercepts of the following line is:

1. $a=\frac{2}{35}$ and $b=-\frac{2}{7}$
2. $a=\frac{35}{2}$ and $b=-\frac{7}{2}$
3. $a=\frac{2}{35}$ and $b=\frac{2}{7}$
4. $a=\frac{35}{2}$ and $b=\frac{7}{2}$

Q.

A(6, 4), B(8, 4), C(10, 6) and D(2, 8) are the vertices of quadrilateral ABCD. Then the point of intersection of its diagonals is

1. $(\frac{5}{7},\frac{2}{7})$

2. $(\frac{15}{7},\frac{19}{7})$

3. $(\frac{50}{7},\frac{32}{7})$

4. $(\frac{15}{7},\frac{32}{7})$

Q.

In the figure, AB = $\sqrt{}units$

__

Q. The centroid of the triangle with vertices at $(-2,-5),(-2,12)$ and $(10,-1)$ is

1. $(3,3)$
2. $(6,6)$
3. $(4,4)$
4. $(2,2)$

Q. A right triangle is formed by connecting the 3 coordinates A, B and C. Find the area of the $\Delta ABC$, if AB and BC are parallel to the coordinate axes as shown in the figure.

1. 6 sq. units
2. 12 sq. units
3. 10 sq. units
4. 20 sq. units

Q. Find the values of a and b if (3, 6) is the centroid of the triangle whose vertices are (2, a), (b, 1), and (1, 4).

1. a = 6, b = 7
2. a = 6, b = 13
3. a = 7, b = -9
4. a = 13, b = 6

Q. The coordinates of three consecutive vertices of a parallelogram are $(1,3),(-1,2)$ and $(2,5).$ The coordinates of the fourth vertex are

1. $(6,4)$
2. $(4,6)$
3. $(-2,0)$
4. none of these

Q. Can the following equation hold simultaneously? $24\frac{x}{2}+\frac{5y}{3}=12,\frac{5x}{4}-\frac{y}{6}=4\&7x-3y=10$

Q. In which quadrant does the point (5, 6) lie?

1. $3^{rd}$ quadrant
2. $1^{st}$ Quadrant
3. $4^{th}$ quadrant
4. $2^{nd}$quadrant

Q. Locate the given coordinates in the XY plane.

1. Quadrant II
2. on the Y-axis
3. on the X-axis
4. Quadrant III

Q.

If centroid of a triangle having two of its vertices $A(1,3),B(2,4)$ is $(0,0)$. Then the third vertex is _______ .

1. $(-3,-7)$

2. $(3,7)$

3. $(-3,7)$

4. $(3,-7)$

Q. Kevin hired a cab and followed the path as shown in the figure. Find the difference between the total distance and displacement covered by him if all the distances in the figure are in kilometers?

Ans - _

Q.

Which of the following statements are correct?

1. Abscissa is the distance from X-axis.

2. Ordinate is the distance from Y-axis.

3. Coordinates of the origin are (0, 0).

4. The first coordinate in the representation of a point is abscissa and the second coordinate is ordinate.

Q. The distance of the point (3 , -2) from the X-axis is .

1. 3 units
2. 2 units
3. -2 units

Q.

What will be the centroid of a triangle whose vertices are (2, 4), (6, 4) and (2, 0)?

1. $\frac{8}{3},\frac{5}{3}$
2. $\frac{7}{2},\frac{5}{2}$
3. $\frac{10}{3},\frac{8}{3}$
4. $\frac{4}{3},\frac{2}{3}$

Q. The centroid of the triangle with vertices (1, 4), (2, 8), and (3, 2) is .

1. $(2,\frac{14}{3})$
2. $(2,\frac{4}{3})$
3. $(3,\frac{1}{3})$